reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem
  for s being 0-started State of SCMPDS
  for i being No-StopCode parahalting Instruction of SCMPDS,
      j being shiftable parahalting Instruction of SCMPDS
 holds IExec(i ';' j,P,s).a = Exec(j,Exec(i, s)).a
proof
  let s be 0-started State of SCMPDS;
  let i be No-StopCode parahalting Instruction of SCMPDS, j be shiftable
  parahalting Instruction of SCMPDS;
  set Mi = Load i;
  thus IExec(i ';' j,P,s).a = IExec(Mi ';' j,P,s).a
    .= Exec(j, IExec(Mi,P,s)).a by Th28
    .= Exec(j, Exec(i, s)).a by Th27;
end;
